"I've not been offered a job, I'm not going to take a job, and I'm not interested in taking a job," Patrick said in a meeting with Texas Realtors. "The lieutenant governor job is the best job in politics and I'm not going anywhere."

Patrick told the realtors group that he has never been interested in working for the Trump administration, despite supporting the president. During the 2016 campaign, Patrick was the Trump campaign's state chairman.

"I told him on Day 1 I have no interest," he said.

Patrick said he's received a handful of concerned calls, including one from a congressman inquiring whether he was leaving Texas to take the job of Homeland Security Secretary Kirstjen Nielsen.

"End that rumor. It's crazy. It's out of control," he said.

But Patrick said he agrees with Trump that border security is a national crisis, calling it an economic, criminal and humanitarian problem. He supports the president's call for a barrier wall, though he said it needs to extend only from Brownsville to Falcon Lake, an area that spans about 161 miles.

"You need a wall, not across 1,900 miles and not across 1,200 miles of Texas," he said. "Where most people come are along the big cities. Whether it's Brownsville, whether it's McAllen, whether it's Laredo, whether it's El Paso, they come through the major areas, they meld into the major population very easily and they disappear."